Flat periodic contact problem for two elastic strips with initial stresses

Abstract

Within the framework of the theory of linearized elasticity, the formulation and solution of the plane load trans fer problem from periodically located elastic stringers to two identical elastic bands with initial (residual) stresses are given. In general, the study is carried out within the theory of large (finite) initial deformations and various versions of the theory of small initial deformations for an arbitrary form of the elastic potential. The influence of initial stresses on the distribution of contact forces in elastic bands and stringers is studied. Proceeding from the assumption that stringers are simultaneously loaded by vertical and horizontal forces, the problem is formulated mathematically as a system of integro-differential equations for the unknown contact stresses. Using the Fourier transformation, the system is solved in a closed form. The stress expressions are represented by quite simple Fourier integrals.